The results of this paper rely heavily on analytic combinatorics [1]}. This framework can also be used to derive uniform random generators (for example with the recursive method [2]} or with a Boltzmann sampler [3]}) directly from the specifications of the classes of phylogenetic networks given below. This could be useful for applications in bioinformatics, especially to generate simulated data in order to evaluate the speed or the quality of the output of algorithms dealing with phylogenetic networks.
